Chancellor of the exchequer George Osborne making his speech at the Conservative party annual conference. Photograph: Christopher Thomond for the Observer

‘I voted Conservative originally because I thought you were going to be the better chance for me and my children. You’re going to cut tax credits after promising you wouldn’t… I can hardly afford the rent I have to pay, I can hardly afford the bills.”

This was the angry accusation made by working mother Michelle Dorrell on BBC One’s Question Time last Thursday. Her outrage is entirely justified: in reversing his promise not to cut tax credits before the election, the prime minister has performed a U-turn far more consequential than any executed by Jeremy Corbyn’s Labour party.

Far from making work pay, analysis by the Institute for Fiscal Studies shows working families with children and eligible for tax credits will be on average £737 a year worse off by 2020. For these families, tax credit cuts dwarf any impact of the government’s “national living wage” of £7.20 an hour from next April for the over-24s. Indeed, expert analysis for the Observer shows that in a two-child family with two parents working full-time, both parents would need to earn £9.55 an hour in 2016 to reach the same standard of living they would have done earning the minimum wage of £6.50 in April 2015.

This represents an impending political problem for the Conservatives: their welfare cuts will seriously hurt parents working long and unsociable hours in low-paid jobs to try to cover rent and bills. Like Michelle Dorrell, many will have voted Conservative at the last election and, many live in the Conservative’s most marginal seats.

It is clear the government – as yet – has little to say to voters who took at face value its pre-election promise not to cut tax credits. Instead, it has sought to obfuscate its impact with a series of misleading claims. George Osborne has audaciously claimed a “typical” family will be £2,000 a year better off by 2020. But this figure falls apart under the lightest of scrutiny: it includes wage growth that would happen anyway and would never normally be taken into account in measuring the impact of a government’s reforms; and an overly generous estimate of the value of the extra entitlement to free childcare, which only applies to parents of three- and four-year-olds, and would be worth much less for families in receipt of tax credits, who would have up to 85% of childcare costs covered anyway.

Osborne has faced unprecedented and bipartisan criticism from the chairs of the Treasury and work and pensions select committees for not publishing a standard distributional analysis alongside his summer budget. In fact, he has announced the Treasury will stop producing these sorts of distributional analyses altogether. The government has also scrapped the official child poverty target and removed income poverty from its suite of poverty measures, a bizarre decision surely designed to try to distract focus from the big increase in the number of working families who will become poor in the coming years.

The extraordinary length to which the government is going to disguise the true impact of tax credits cuts is not only wrong – it is politically reckless. Millions of families are going to be hundreds of pounds a year worse off next April; many will have not yet realised what these changes mean for them personally. When families up and down the country feel the pinch, Osborne’s claims about “typical” families will feel insultingly irrelevant.

Not only is the national living wage nowhere near at the rate it would need to be to compensate families for losses to tax credits, the government has no plan to improve productivity and innovation in low-wage sectors such as retail and care. This means the national living wage will at best result in greater bunching of wages around this new minimum, with little impact for those who earn just above it, but at worst, in job losses, as predicted by the Office for Budget Responsibility. A real plan to make work pay in the lower half of the distribution would be based not just on increases in the minimum wage, but also on improving management and job quality in shops and care homes, and improving returns to intermediate skills.

In service sectors such as care, consumers also need to be prepared to pay more to reflect the true value of the service they receive. Yet government is by far the biggest consumer of both social care and childcare, and both sectors will experience a serious squeeze as a result of deep cuts to social care and insufficient government funding for the expansion of free childcare. The care sector is already one of the worst in terms of minimum wage compliance, a combination of the national living wage plus cuts to funding risks making this even worse.

Focusing on productivity is even more critical in the face of long-term downward pressures on wages in low-paid jobs. While technological progress will continue to drive growth, it also increases inequality by boosting the returns to capital and high-skill work at the expense of the lower paid. Technologies such as driverless cars look set to replace taxi drivers and hauliers in the next couple of decades but will also create jobs – for different people with different sets of skills. We are also likely to see increasing numbers of people who are self-employed, fuelled by the growth of online platforms such as TaskRabbit and Uber – people who will be unprotected by minimum wage and other employment legislation.

No amount of concealment can disguise the fact that this government is forcing hard-working parents in low-paid jobs to pay for tax cuts for the comfortably affluent and the very wealthy. For once, the politics and the ethics point in the same direction. The government must reverse giveaways to cushion the impact of its tax credit cuts. Not to do so would be to make a ridicule of Cameron’s bold claim last week that the Conservatives will be “the party for working people – today, tomorrow, always”.